I think as shown by similar scandals at NYT and WSJ, that the media press do not accept feedback, and instead will rally around extending and furthering their ideological anti-liberal (authoritarian) monoculture, and instead get rid of dissenting voices.
see James Bennet at NYT (who was fired for publishing a op-ed from a sitting American senator) or even Kevin D. Williamson at the Athletic.
I can't see why everybody got so worked up about the op-ed you're referring to. The Times has traditionally been a venue for voices that are not in its constituency, and in this particular case, Cotton wrote such a crazy article that it reduced his credibility significantly in front of the nation.
He proposed using the military to quell protests, https://www.nytimes.com/2020/06/03/opinion/tom-cotton-protes...
I think if all op-eds published in the Times were inspected for factual accuracies, they'd find plenty in the ones that align with the Times's employees (the Cotton op-ed has a long preface which basically says "we shouldn't have published this because facts")
see James Bennet at NYT (who was fired for publishing a op-ed from a sitting American senator) or even Kevin D. Williamson at the Athletic.